Proposition 13

Tag 0BFE, permanent. Cite it as [Bourbaki, Tag 0BFE].

General Topology, chapter II, § 3. Complete spaces

If Y is a complete Hausdorff uniform space and X a dense subspace of Y, then the canonical injection $X \to Y$ extends to an isomorphism of $\hat{X}$ onto Y.

For every uniformly continuous mapping of X into a complete Hausdorff uniform space Z extends uniquely to a uniformly continuous mapping of Y into Z by Theorem 2 of no. 6.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Theorem 2